scholarly journals On the Navier–Stokes system with the Coulomb friction law boundary condition

2016 ◽  
Vol 68 (1) ◽  
Author(s):  
Loredana Bălilescu ◽  
Jorge San Martín ◽  
Takéo Takahashi
Keyword(s):  
Boundary Condition ◽  
Coulomb Friction ◽  
Stokes System ◽  
Navier Stokes ◽  
Friction Law ◽  
Coulomb Friction Law

Some Consequences of Coulomb Friction in Modeling Longitudinal Traction

1990 ◽  
Vol 18 (1) ◽  
pp. 13-65 ◽  
Author(s):  
W. W. Klingbeil ◽  
H. W. H. Witt
Keyword(s):  
Shear Force ◽  
Coulomb Friction ◽  
Interfacial Shear ◽  
Force Generation ◽  
Behavior Patterns ◽  
Inflation Pressure ◽  
Friction Law ◽  
The Coefficient Of Friction ◽  
Coulomb Friction Law ◽  
Perfect Adhesion

Abstract A three-component model for a belted radial tire, previously developed by the authors for free rolling without slip, is generalized to include longitudinal forces and deformations associated with driving and braking. Surface tractions at the tire-road interface are governed by a Coulomb friction law in which the coefficient of friction is assumed to be constant. After a brief review of the model, the mechanism of interfacial shear force generation is delineated and explored under traction with perfect adhesion. Addition of the friction law then leads to the inception of slide zones, which propagate through the footprint with increasing severity of maneuvers. Different behavior patterns under driving and braking are emphasized, with comparisons being given of sliding displacements, sliding velocities, and frictional work at the tire-road interface. As a further application of the model, the effect of friction coefficient and of test variables such as load, deflection, and inflation pressure on braking stiffness are computed and compared to analogous predictions on the braking spring rate.

On Some Problems With Modeling of Coulomb Friction in Self-Locking Speed Reducers

2014 ◽  
Author(s):  
Marek Wojtyra
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Equations Of Motion ◽  
Velocity Ratio ◽  
Friction Forces ◽  
Friction Law ◽  
Rigid Body Model ◽  
Feasible Sets ◽  
Unstable Solutions ◽  
Coulomb Friction Law

A simple mathematical model of friction in speed reducers is presented and discussed. A rigid body approach, typical for multibody simulations, is adopted. The model is based on the Coulomb friction law and exploits the analogy between reducers and wedge mechanisms. The first version of the model is purely rigid, i.e. no deflections of the mechanism bodies are allowed. Constraints are introduced to maintain the ratio between input and output velocity. It is shown that when friction is above the self-locking limit, paradoxical situations may be observed when kinetic friction is investigated. For some sets of parameters of the mechanism (gearing ratio, coefficient of friction and inertial parameters) two distinct solutions of normal and friction forces can be found. Moreover, for some combinations of external loads, a solution that satisfies equations of motion, constraints and Coulomb friction law does not exist. Furthermore, for appropriately chosen loads and parameters of the mechanism, infinitely many feasible sets of normal and friction forces can be found. Examples of all indicated paradoxical situations are provided and discussed. The second version of the model allows deflection of the frictional contact surface, and forces proportional to this deflection are applied to contacting bodies (no constraints to maintain the input-output velocity ratio are introduced). In non-paradoxical situations the obtained results are closely similar to those predicted by the rigid body model. In previously paradoxical situations no multiple solutions of friction force are found, however, the amended model does not solve all problems. It is shown that in regions for which the paradoxes were observed only unstable solutions are available. Numerical examples showing behavior of the model are provided and analyzed.

scholarly journals Stationary Navier–Stokes equations with non-homogeneous boundary condition in a system of two connected layers

2012 ◽  
Vol 53 ◽  
Author(s):  
Kristina Kaulakytė
Keyword(s):  
Boundary Condition ◽  
Boundary Problem ◽  
Stokes System ◽  
Stokes Equations ◽  
Boundary Value ◽  
Homogeneous Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

In this paper the stationary Navier–Stokes system with non-homogeneous boundary condition is studied in domain which consists of two connected layers. The extension of the boundary value, which reduces the non-homogeneous boundary problem to the homogeneous one, is constructed in this paper.

scholarly journals Crack in a solid under Coulomb friction law

2000 ◽  
Vol 45 (4) ◽  
pp. 265-290 ◽  
Author(s):  
Victor A. Kovtunenko
Keyword(s):  
Coulomb Friction ◽  
Friction Law ◽  
Coulomb Friction Law

Use of the Coulomb friction law in solving contact problems by the finiteelement method

1986 ◽  
Vol 18 (2) ◽  
pp. 245-250 ◽  
Author(s):  
V. I. Zaitsev ◽  
V. M. Shchavelin
Keyword(s):  
Coulomb Friction ◽  
Contact Problems ◽  
Friction Law ◽  
Coulomb Friction Law

scholarly journals ON THE SENSITIVITY OF THE NONLINEAR TERM IN THE OUTFLOW BOUNDARY CONDITION

2021 ◽  
Vol 61 (SI) ◽  
pp. 117-121
Author(s):  
Tomáš Neustupa ◽  
Ondřej Winter
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Stokes System ◽  
Nonlinear Term ◽  
Navier Stokes ◽  
Outflow Boundary Condition ◽  
Flow Through ◽  
Outflow Boundary

This paper studies the artificial outflow boundary condition for the Navier-Stokes system. This type of condition is widely used and it is therefore very important to study its influence on a numerical solution of the corresponding boundary-value problem. We particularly focus on the role of the coefficient in front of the nonlinear term in the boundary condition on the outflow. The influence of this term is examined numerically, comparing the obtained results in a close neighbourhood of the outflow. The numerical experiment is carried out for a fluid flow through the channel with so called sudden extension. Presented numerical results are obtained by means of the OpenFOAM toolbox. They confirm that the kinetic energy of the flow in the channel can be controlled by means of the proposed boundary condition.

New theoretical model of stress transfer between fibre and matrix in a uniaxially fibre-reinforced composite

1989 ◽  
Vol 425 (1868) ◽  
pp. 215-244 ◽  
Keyword(s):  
Boundary Conditions ◽  
Coulomb Friction ◽  
Stress Transfer ◽  
Matrix Crack ◽  
Matrix Interface ◽  
Friction Law ◽  
Reinforced Composite ◽  
Coulomb Friction Law ◽  
Frictional Slip ◽  
Fibre Matrix

A new analytical method has been developed that can predict the stress transfer between fibre and matrix in a uniaxially fibre-reinforced composite associated with either a single matrix crack or a fibre break. Account is taken of thermal residual stresses arising from a mismatch in thermal expansion coefficients between the fibre and matrix. In addition Poisson ratio mismatches are also taken into account. The theoretical approach retains all relevant stress and displacement components, and satisfies exactly the equilibrium equations, the interface conditions and other boundary conditions involving stresses. Two of the four stress-strain-temperature relations are satisfied exactly, whereas the remaining two are satisfied in an average sense. The required non-interface displacement boundary conditions are also satisfied in an average sense. The general representation is used to solve three types of stress transfer problem. A matrix crack and a broken fibre are analysed for the case when there is perfect bonding between fibre and matrix. The third type of problem takes account of frictional slip at the interface governed by the Coulomb friction law. The approximate analytic approach described in this paper, and the preliminary numerical predictions presented, indicate that the stress transfer between fibres and matrix in a unidirectional fibre-reinforced composite, loaded in tension, can now be investigated theoretically in more detail than before. The paper includes some discussion of singularities in the stress fields, which are smoothed by the averaging techniques employed in the analysis. The analytical approach has enabled the development of a micro-mechanical model of frictional slip at the fibre-matrix interface based on the Coulomb friction law, which is more realistic than assuming that the interfacial shear stress is a constant. Predictions are presented of the stress distributions along the fibre-matrix interface and, in particular, it is shown how the length of the frictional slip zone is related to applied strain, friction coefficient, fibre volume fraction and the difference between the test and ‘manufacturing’ temperatures. An indication is given of many other areas of composite modelling where the new theory will be applied.

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